One of the most difficult things for young musicians is practicing. It's boring, they say. Parents are frequently so frustrated that they're ready to give up on the instrument. However, with a little cooperation between parents and teachers, motivating young musicians to practice isn't too difficult.
First, realize that young kids have short attention spans. Practicing for more than 15 minutes at a time is going to impossible for most young kids. Pushing them to practice too long is going to make them reluctant to practice at all. Remember: it's better that your child pick up his instrument for five minutes than not at all, so encourage him to play but don't push for time limits.
Young kids also learn through play. Don't try to make practice times too structured for the kids; they want to play around and figure out how things work and what they're capable of. Making them repeat specific skills or practice in a logical, orderly way (as an adolescent or adult might) will bore them. Encourage them to play the instrument as much as they would like and to take the time to "figure it out." If you, as a parent, know how to play the instrument, occasionally issue gentle reminders like, "Where is your hand position? Did those notes sound right to you?" Don't correct them; let them see if they can figure it out alone. Usually, they can (with the gentle reminder).
Don't expect perfection. A young child might have learned something as well as he is going to learn it, because he simply doesn't have the motor skills yet to learn it any better. Accept this and help him to discover more. If you're not sure what your child should be capable of at a particular age or skill level, ask your child's teacher.
If your child wrinkles his nose at the word "practice," ask him instead, "Will you play for me?" The end result is the same, but the child is much more obliged to obey. (This works -- a 9 year-old refused to "practice" at her mother's insistence, but was more than happy to "play for" her father at his request.)
Offer rewards (in conjunction with the teacher, if it's a private lesson situation). For example, Johnny gets a sticker for every ten minutes he practices. After ten stickers, gets a small toy. Cost to you: $2 - $3. Reward for him: 100 minutes of practice time and new skills learned during that time.
Remember that young children don't do well with intrinsic motivation. They don't yet see how practicing an instrument will help them in the future. Beyond that, they live pretty much in the moment! Offering rewards is a form of extrinsic motivation that will keep them interested long enough to develop intrinsic motivation.
Expect to see the development of intrinsic motivation around 10 or 12, especially if your child has already been playing for several years.
Another caution: NEVER make practice into a punishment. Statements like, "You can't go play with your friends until you practice" makes playing with friends desirable, and practicing undesirable. If you treat practicing this way, it becomes a chore, and you have ruined it for the young child. Always make practice seem positive (as a small joke, you may even say, "You can't practice until you make your bed!"). Your child will pick up on your attitude toward the instrument and toward practice, so make sure it seems fun.
The final thing you can do is to play music frequently. Play classical music or anything that prominently features your child's instrument. This is often motivation for children to work hard, because they want to "sound like that" someday. Also, listening to music helps them to understand music, which can help their overall musical skills.
If you motivate your young musician to practice now, he will be far better off in the future in so many different ways. More talented, more disciplined, and possibly more intelligent. Music, and motivation, are very important.